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  2. Integral of the secant function - Wikipedia

    en.wikipedia.org/wiki/Integral_of_the_secant...

    The integral of the secant function was historically one of the first integrals of its type ever evaluated, before most of the development of integral calculus. It is important because it is the vertical coordinate of the Mercator projection , used for marine navigation with constant compass bearing .

  3. List of integrals of hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    3.1 Integrals of hyperbolic tangent, cotangent, secant, cosecant functions 3.2 Integrals involving hyperbolic sine and cosine functions 3.3 Integrals involving hyperbolic and trigonometric functions

  4. List of integrals of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    For the special antiderivatives involving trigonometric functions, see Trigonometric integral. [ 1 ] Generally, if the function sin ⁡ x {\displaystyle \sin x} is any trigonometric function, and cos ⁡ x {\displaystyle \cos x} is its derivative,

  5. Integral of secant cubed - Wikipedia

    en.wikipedia.org/wiki/Integral_of_secant_cubed

    This is one of several integrals usually done in a first-year calculus course in which the most natural way to proceed involves integrating by parts and returning to the same integral one started with (another is the integral of the product of an exponential function with a sine or cosine function; yet another the integral of a power of the ...

  6. List of integrals of inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    For a complete list of integral formulas, see lists of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration. For each inverse hyperbolic integration formula below there is a corresponding formula in the list of integrals of inverse trigonometric functions.

  7. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.

  8. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle...

    The substitution is described in most integral calculus textbooks since the late 19th century, usually without any special name. [5] It is known in Russia as the universal trigonometric substitution , [ 6 ] and also known by variant names such as half-tangent substitution or half-angle substitution .

  9. Integration using Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Integration_using_Euler's...

    At this point we can either integrate directly, or we can first change the integrand to 2 cos 6x − 4 cos 4x + 2 cos 2x and continue from there. Either method gives Either method gives ∫ sin 2x cos ⁡ 4 x d x = − 1 24 sin ⁡ 6 x + 1 8 sin ⁡ 4 x − 1 8 sin ⁡ 2 x + C . {\displaystyle \int \sin ^{2}x\cos 4x\,dx=-{\frac {1}{24 ...